The estimation of phylogenetic trees from molecular sequences (e.g., DNA, RNA, or amino acid sequences) is a major step in many biological research studies, and is typically approached using heuristics for NP-hard optimization problems. In this talk, I will describe a new approach for computing large trees: constrained exact optimization. In a constrained exact optimization, we implicitly constrain the search space by providing a set X of allowed bipartitions on the species set, and then use dynamic programming to find a globally optimal solution within that constrained space. For many optimization problems, the dynamic programming algorithms can complete in polynomial time in the input size. Simulation studies show that constrained exact optimization also provides highly accurate estimates of the true species tree, and analyses of both biological and simulated datasets shows that constrained exact optimization provides improved solutions to the optimization criteria efficiently. We end with some discussion of future research in this topic. (Refreshments will be served before the talk at 10:30.)